Multiple bubble dynamics and velocity selection in Laplacian growth without surface tension

Mark Mineev-Weinstein; Giovani L. Vasconcelos

doi:10.1016/j.physd.2023.134032

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arXiv · 1501.01052

Multiple bubble dynamics and velocity selection in Laplacian growth without surface tension

Mark Mineev-Weinstein·Giovani L. Vasconcelos

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Abstract

A new selection phenomenon in nonlinear interface dynamics is predicted. A generic class of exact regular unsteady multi-bubble solutions in a Hele-Shaw cell is presented. These solutions show that the case where the asymptotic bubble velocity, $U$, is twice greater than the velocity, $V$, of the uniform background flow, i.e., $U = 2V$, is the only attractor of the dynamics. Contrary to common belief, the predicted velocity selection requires neither surface tension nor other external regularization.

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Mark Mineev-Weinstein, Giovani L. Vasconcelos. 2015-01-06. Multiple bubble dynamics and velocity selection in Laplacian growth without surface tension. https://doi.org/10.1016/j.physd.2023.134032

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